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I went from a biology degree to engineering, and I was lucky enough to find a program that let me take some extra math classes in conjunction with my grad courses. It sounds like if it's very competitive that may not be an option. If I were you, I'd search every program in the country and find the ones with the fewest or most flexible pre-reqs, and apply to them all, or start taking remedial courses, or find another engineering or biology graduate option if applying doesn't work.
To get into biomedical; you need to get the Engineering courses: math, physics, mechanics, fluid dynamics, heat transfer, systems engineering, etc. I have a typical liberal arts course work for biology, you are looking at two to three years of heavy course load to have a competitive chance. BioMedical Engineering is more Engineering than Biology.